Local and Global Solvability for Advection-Diffusion Equation on an Evolving Surface with a Boundary
Analysis of PDEs
2022-12-14 v1
Abstract
This paper considers the existence of local and global-in-time strong solutions to the advection-diffusion equation with variable coefficients on an evolving surface with a boundary. We apply both the maximal -in-time regularity for Hilbert space-valued functions and the semigroup theory to construct local and global-in-time strong solutions to an evolution equation. Using the approach and our function spaces on the evolving surface, we show the existence of local and global-in-time strong solutions to the advection-diffusion equation. Moreover, we derive the asymptotic stability of the global-in-time strong solution.
Cite
@article{arxiv.1904.03785,
title = {Local and Global Solvability for Advection-Diffusion Equation on an Evolving Surface with a Boundary},
author = {Hajime Koba},
journal= {arXiv preprint arXiv:1904.03785},
year = {2022}
}